We consider a non degenerate quasilinear parabolic stochastic partial differential equation with a uniformly elliptic diffusion matrix. It is driven by a nonlinear noise. We study regularity properties of its weak solution satisfying classical a priori estimates. In particular, we determine conditions on coefficients and initial data under which the weak solution is Hölder continuous in time an...

+ c(y) = u in Ω× (0, T ), assuming that the solution of an associated boundary value problem is known at the terminal time, y(x, T ), over a (probably small) subset of Ω, for each source term u. Our work can be divided into two parts. Firstly, the uniqueness of A,~b and c is proved under appropriate assumptions. Secondly, we consider a finite-dimensional optimization problem that allows for the...

Abstract We prove a-posteriori error-estimates for reduced-order modeling of quasilinear parabolic PDEs with non-monotone nonlinearity. consider the solution a semi-discrete in space equation as reference, and therefore incorporate reduced basis-, empirical interpolation-, time-discretization-errors our consideration. Numerical experiments illustrate results.

Abstract The global existence of weak solutions to a class quasilinear parabolic equations with nonlinearities depending on first order terms and integrable data in moving domain is investigated. includes the p -Laplace equation as special case. Weak are shown be by obtaining appropriate estimates gradient well suitable version Aubin–Lions lemma domains.

This paper is devoted to prove analyticity of stable invariant manifold in a neighbourhood of an unstable steady-state solution for GinzburgLandau equation defined in a bounded domain of dimension not more than three. This investigation is made for possible applications in stabilization theory for semilinear parabolic equation. Introduction In this paper we prove analyticity of stable invariant...